Separation of variables in the Baxter-Bazhanov-Stroganov model

Abstract:
The Baxter-Bazhanov-Stroganov model (also known as the t² model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic L-operators. Using the latter formulation and the Sklyanin-Kharchev-Lebedev approach, we give the explicit derivation of the eigenvectors of the component B_n(l) of the monodromy matrix for the fully inhomogeneous chain of finite length. For the periodic chain we obtain the Baxter T-Q-equations via separation of variables. The functional relations for the transfer-matrices of the t² model guarantee non-trivial solutions to the Baxter equations. For the N=2 case, which is free fermion point of a generalized Ising model, the Baxter equations are solved explicitly. These solutions give explicit formulas for eigenvectors of Ising transfer-matrix. Using them, we proved formula for form-factors in the Ising model on finite lattice.

Joint work with G. von Gehlen, S. Pakuliak, V. Shadura, Yu. Tykhyy.